Representation of Eddies in Primitive Equation Models by a PV Flux

Richard Wardle MIT/WHOI Joint Program, Massachusetts Institute of Technology, Cambridge, Massachusetts

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John Marshall Program in Atmospheres, Oceans and Climate, Massachusetts Institute of Technology, Cambridge, Massachusetts

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Abstract

The parametric representation of buoyancy and momentum transport by baroclinic eddies in a primitive equation “β plane” channel is studied through a transformation of the governing equations. Adoption of the“transformed Eulerian mean” and the assumption that the eddies (but not the mean flow) are quasigeostrophic in nature leads to 1) the eddies being represented symbolically by one term, an eddy potential vorticity flux, rendering a representation that incorporates both eddy momentum and eddy buoyancy fluxes, and 2) the advecting velocities being those of the residual mean circulation. A closure is employed for the eddy potential vorticity flux that directs it down the mean potential vorticity gradient. Care is taken to ensure that the resulting force does not generate any net momentum in the channel but only acts to redistribute it.

The approach is investigated by comparing a zonally averaged parameterized model with a three-dimensional eddy-resolving calculation of flow in a stress-driven channel. The stress at the upper surface is communicated down the water column to the bottom by eddy form drag. Moreover, lateral eddy momentum fluxes act to strengthen and sharpen the mean flow, transporting eastward momentum from the flanks to the center of the jet, up its large-scale gradient. Both vertical momentum transfer and lateral, upgradient momentum transfer by eddies, is captured in the parameterized model.

Finally, advantages of the parametric approach are demonstrated in two further contexts: 1) the spindown of a baroclinic zone and 2) the maintenance of surface winds by eddy momentum flux in the atmosphere.

Corresponding author address: Richard Wardle, Department of Geophysical Sciences, University of Chicago, Chicago, IL 60637.

Email: rmwardle@geosci.uchicago.edu

Abstract

The parametric representation of buoyancy and momentum transport by baroclinic eddies in a primitive equation “β plane” channel is studied through a transformation of the governing equations. Adoption of the“transformed Eulerian mean” and the assumption that the eddies (but not the mean flow) are quasigeostrophic in nature leads to 1) the eddies being represented symbolically by one term, an eddy potential vorticity flux, rendering a representation that incorporates both eddy momentum and eddy buoyancy fluxes, and 2) the advecting velocities being those of the residual mean circulation. A closure is employed for the eddy potential vorticity flux that directs it down the mean potential vorticity gradient. Care is taken to ensure that the resulting force does not generate any net momentum in the channel but only acts to redistribute it.

The approach is investigated by comparing a zonally averaged parameterized model with a three-dimensional eddy-resolving calculation of flow in a stress-driven channel. The stress at the upper surface is communicated down the water column to the bottom by eddy form drag. Moreover, lateral eddy momentum fluxes act to strengthen and sharpen the mean flow, transporting eastward momentum from the flanks to the center of the jet, up its large-scale gradient. Both vertical momentum transfer and lateral, upgradient momentum transfer by eddies, is captured in the parameterized model.

Finally, advantages of the parametric approach are demonstrated in two further contexts: 1) the spindown of a baroclinic zone and 2) the maintenance of surface winds by eddy momentum flux in the atmosphere.

Corresponding author address: Richard Wardle, Department of Geophysical Sciences, University of Chicago, Chicago, IL 60637.

Email: rmwardle@geosci.uchicago.edu

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